You're provided with a bottle labled [CoCl2.6H2O] = 0.056 M in 4.60 M HCl. You heat a small volume of the solution in a hot water bath to 50 ∘C. If you determine that [CoCl42-] = 0.031 M at 50 ∘C at equilibrium, what must be the equilibrium concentration of [Cl-] at 50 ∘C?

The equilibrium concentration of Cl⁻ at 50°C is 4.54 M, after the solution of 0.056 M CoCl₂·6H₂O with 4.60 M HCl is heated in a water bath to 50°C. It was calculated knowing that the equilibrium concentration of CoCl₄²⁻ at 50°C is 0.031 M.  

The reaction between CoCl₂·6H₂O and HCl is the following:

CoCl₂·6H₂O + 2HCl → H₂CoCl₄ + 6H₂O

The initial concentrations are:

[CoCl₂·6H₂O] = 0.056 M

[HCl] = 4.60 M

At equilibrium, we have:

CoCl₂·6H₂O + 2HCl → H₂CoCl₄ + 6H₂O

0.056-x        4.60-2x         x            6x

We know that the CoCl₄²⁻ concentration at equilibrium is 0.031 M, so:            

With this, we can find the equilibrium concentration of Cl⁻ and CoCl₂·6H₂O:

Therefore, the equilibrium concentration of Cl⁻ is 4.54 M.

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Equilibrium concentration of at is 4.538 M

Explanation:

Initial concentration of = 0.056 M

Initial concentration of = 4.60 M

The given balanced equilibrium reaction is,

Initial conc.          0.056 M      4.60 M        0 M       0 M

At eqm. conc.     (0.056-x) M   (4.60-2x) M   (x) M    (6x) M

The expression for equilibrium constant for this reaction will be,

Given : equilibrium concentration of =x =  0.031 M

Concentration of = (4.60-2x) M  = =4.538 M  

Thus equilibrium concentration of at is 4.538 M

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